Integral representations for the Hartman--Watson density
Probability
2021-04-07 v3
Abstract
This paper concerns the density of the Hartman--Watson law. Yor (1980) obtained an integral formula that gives a closed-form expression of the Hartman--Watson density. In this paper, based on Yor's formula, we provide alternative integral representations for the density. As an immediate application, we recover in part a Dufresne's result (2001) that exhibits remarkably simple representations for the laws of exponential additive functionals of Brownian motion.
Cite
@article{arxiv.1904.00595,
title = {Integral representations for the Hartman--Watson density},
author = {Yuu Hariya},
journal= {arXiv preprint arXiv:1904.00595},
year = {2021}
}
Comments
21 pages; this is an abridged version of the previous one, accepted for publication in the Journal of Theoretical Probability, with shortened Section 4